Average Error: 58.0 → 0.0
Time: 15.9s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[\tanh x\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\tanh x
double f(double x) {
        double r1722427 = x;
        double r1722428 = exp(r1722427);
        double r1722429 = -r1722427;
        double r1722430 = exp(r1722429);
        double r1722431 = r1722428 - r1722430;
        double r1722432 = r1722428 + r1722430;
        double r1722433 = r1722431 / r1722432;
        return r1722433;
}
↓
double f(double x) {
        double r1722434 = x;
        double r1722435 = tanh(r1722434);
        return r1722435;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied tanh-undef0.0

    \[\leadsto \color{blue}{\tanh x}\]

  4. Final simplification0.0

    \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))